Numbers Can Lie

Context needs to be part of any mathematical equation. “Narratives without statistics are blind, statistics without narratives are empty.” Steven Pinker, the author of The Better Angels of Our Nature, describes this paradox perfectly.

Most people suffer from something called denominator bias. This means they focus on the top number of a fraction, the numerator. They ignore the bottom one, the denominator. This leads to some very interesting conclusions that often have nothing to do with reality.

Combine this with recency bias which greatly overweights the influence of current events and we have a big problem.

Let’s look at a common statement about history that 95% of the population would agree with: “The 20th century was the bloodiest in history.”

The number people look at is the TOTAL deaths rather than the population-adjusted number. While this is certainly no consolation to those slain in the brutal wars of this period, it is not something to be ignored. In other words, there were a few billion more people around at this time compared to say the 8th century.

Denominator bias rears its ugly head again.

It turns out the 8th century may have the most violent in human history when the all-important size of the world’s total population at the time is taken into account. There was something called the Lushan Revolt in China. This was a horrifically bloody Civil War against the ruling Tang Dynasty, When this blood bath was over, 40 million people lay dead. This was equivalent to 1/6 of the world’s population at the time. The adjusted mid-20th-century number would be 429 million people.

Numbers can lie, if you let them.

As a matter of fact, the second most bloody event occurred during the 13th century during the Mongol Conquests. This killed 40 million people in real time. Adjust this number for the current world’s population and the number balloons to 278 million!

To be fair, I did not know any of this. That is why I read books by people who are a lot smarter than me.

Does this all relate to investors’ attitudes towards numbers related to the market? Absolutely.

For instance, in October of 1987, the market fell 22% in one day. This was equivalent to 507 Dow points. Flash forward to July 2017. If the Dow were to fall 507 points next week, the legions of gloom would be screaming about another 1987-like melt down.

Really? The Dow today is 21,575 as of July 17. A 507 decline would be equivalent to a 2.35% daily loss; unpleasant, but 10 times less so than the carnage experienced on that fateful October day.

Numbers can lie, if you let them.

We hear all the time about how in 1980, people could get a 15% C.D.; instead of lamenting for these “good old days,” here is something to ponder. Is a 15% C.D. really better than the current 2017 2.0% miserly version?

Context is the answer. In 1980, inflation hovered around 14.8%. Today, the inflation rate is about 1.7%. When you adjust for inflation the real returns for a 15% C.D. and today’s 2.0% version are virtually identical.

Numbers can lie, if you let them.

Every day I hear about unscrupulous insurance salesmen who tell teachers they are “only” paying 2-3% on their investments. Sounds like a pretty small number. What these deceivers don’t tell their prey is: Historically, inflation hovers around 3%. If returns going forward are expected to be around 7%, real returns after inflation will be about 4%.

Why am I boring you with this minutia?

Subtract 3% in costs, and many teachers end up giving away 75% of their returns in fees. Denominator bias at work again.

The numbers will lie, if you let them.

Finally, the American Action Forum tried to pull a fast one trying to prove that most consumer complaints against the financial industry are baseless.

According to The Intercept, “…the report said that consumers filed nearly 4,000 arbitration cases last year with FINRA, the Financial Industry Regulatory Authority, alleging wrongdoing by brokers, but that only 158 — about 4%— of those cases were decided in favor of the consumer.”

But Milloy’s denominator was off by a factor of 10. Only 389 cases were decided by arbitrators in 2016, meaning that those 158 customers who won represented 41% of the cases decided by arbitrators. The reference to the 158 customer wins appeared on a FINRA chart which clearly shows that customers had won 41% of the cases they brought, out of 389 cases decided, not Milloy’s “nearly 4,000.”

The combination of denominator bias combined with historical myopia and downright dishonesty is a deadly combination.